That does look like cold damage to me. The dark spots are definitely something that I see on my outdoor palms when the weather gets cold. They won't go away, but will not hurt the plant long term unless the exposure to cold continues.
Maybe check with the maintenance people at the hotel about the doors being left open, and ask if the palms can be moved away from the cold air if/when they need to air out the place? At high altitude, like most of Colorado, the air is also even more dry than lower down, because the thinner air can hold a lot less moisture. So while the doors are closed, the pool is probably keeping the area fairly humid, when they air out the enclosure, suddenly your palms are exposed not only to cold, but also to very dry air.
(I lived in Utah for 21 years, skiing there is very thirsty exercise!)
